The energy levels of the first few low-lying states of carbon in intense magnetic fields upwards of approximate to 10(7) T are calculated in this study. We extend our previously employed pseudospectral approach for calculating the eigenstates of the carbon atom. We report data for the ground state and a low-lying state that are in good agreement with findings elsewhere, as well as additional data for ten other states of the carbon atom. It is seen that these latter states also become strongly bound with increasing magnetic field strengths. The data presented in this study are relevant for astrophysical applications, such as magnetized white dwarf and neutron star spectral analysis as well as opacity calculations and absorption features, including in the context of material accreting onto the surfaces of these compact objects.